Question

if y varies directly with the square root of x and inversely with z, what is the constant of proportionality if y=27 when x=9 and z=6

Answer 1

Since y varies directly with the square root of x and inversely with z, then the equation that relates x, y and z has the form:

`y=k\cdot(x^2)/(z)`

To find the value of the constant of proportionality k, substitute the given values of x, y and z:

`\begin{gathered} 27=k\cdot(9^2)/(6) \\ \Rightarrow27=k\cdot(81)/(6) \\ \Rightarrow k=(6\cdot27)/(81) \\ \Rightarrow k=2 \end{gathered}`

Therefore, the value of the constant of proportionality, is:

`2`